In many industrial and optical computing applications, it is necessary to reconstruct an object's complete description from a partial description. Systems for performing such image reconstruction are expected to have an a priori knowledge of the object image to be reconstructed. To fully utilize parallelism of optics, the memory elements should be such that they can be accessed simultaneously and in parallel on the basis of data content rather than by specific address or location. Such a memory, referred to as an associative memory, delivers, the output even when it is stimulated by a partial image input of the stored information. The mechanics of storing, matching, and decision making determines the actual performance of the associative memory.
Hopfield has described a memory matrix that is easy to implement and requires very little time for learning and retrieval. J. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," Proc. Natl. Acad. Sci. USA 79, 2554-2558 (1982). The prior art reveals several implementations of this model in which only bipolar binary numbers (1,-1) were used for storing vectors and unipolar binary numbers (1,0) were used to address the memory. N. H. Farhat, D. Psaltis, A. Prata and E. Paek, "Optical implementation of the Hopfield model," Appl. Opt. 24(10), 1469-1475 (1985) and B. Macukow and H. H. Arsenault, "Modification of the threshold condition for a content-addressable memory based on the Hopfield model," Appl. Opt. 26(1), 34-36 (1986). Several different modifications to this initial work of Hopfield have already been proposed, and there have been several reported studies on various number representations of neurons. J. S. Bayley and M. A. Fiddy, "On the use of the Hopfield model for optical pattern recognition," Opt. Commun. 64, 105-110 (1987) and M. Takeda and J. W. Goodman, " Neural networks for computation: number representations and programming complexity," Appl. Opt. 25(18), 3303-3046 (1986).
The Hopfield model uses the outer product of a vector with itself as a memory matrix for that vector and thereafter adds such memory matrices of each of the nearly orthogonal stored vectors. An inner-product associative memory has been proposed based on Hopfield's model (with autoneural interconnect). S. Y. Kung and H. K. Liu, "An optical inner-product array processor for associative retrieval," Proc. SPIE, Vol. 613, Nonliner Optics and Applications, 214-219 (1986). For matching and retrieval, the memory is addressed by an input vector V.sup.in. Accordingly, the ith element of the estimated vector V.sup.es is given by ##EQU1## where V.sub.p.sup.st,m represents the pth element of the mth stored vector and n is the length of the vectors.
The convergence mechanism of vectors in Hopfield's neural network in relation to recognition of partially known patterns has been studied in terms of both inner products and Hamming distance, the measure of similarity between objects. In much of the prior art, the Hamming distance has been used as a measure of dissimilarity, overlooking the role of the inner products in determining convergence. In cases other than that of the bipolar binary input, the Hamming distance criterion does not directly represent the ongoing matching process of convergence. Inner-product weighting coefficients play a more dominant role in many data representations for determining the convergence mechanism.
Each of the input representations, bipolar binary and unipolar binary, has its own merit. With bipolar binary input and thresholding, the convergence outcome of the associative memory always agrees with the minimum Hamming distance criterion. At the same time, the bipolar binary representation prevents the input from converging to a negative vector. On the other hand, the use of binary unipolar representation seems to recognize a partial input vector irrespective of its Hamming distance.
Recently it has been shown that in cases other than that of the bipolar binary input, the Hamming distance criterion does not directly represent the ongoing matching process of convergence. A. A. S. Awwal, M. A. Karim and H. K. Liu, "Associative memory: an optimum binary neuron representation," Proc. SPIE, Vol. 1053, Optical Pattern Recognition, 17-29, (1989). An object of this invention is to provide associative memory using trinary neuron representation which overcomes these discrepancies. The resulting trinary associative memory may be used to process one dimensional as well as two-dimensional stored images, such as those encountered in industrial applications.